Soon after the sun had set – late tangerine rays stroking the canvas of tipis encamped in bitter cold above the sea – the tribe converged on Seaton Town Hall in Devon, no less, and the headline act at Easter's big festival began. Forget the Stones' date at Glastonbury up the road; here's the band that is the real guardian of British rock, enduring but ever-mutating, and – as the weekend's music demonstrated – ever-improving: Hawkwind.

There is a crucial difference between Hawkwind's following and that of other groups spawned in the 1960s: while the great survivors and revivers have their elder and younger fans, the originals and their children, no other has collected a seamless following at – and recruited musicians from – every musical stage along the way, from 60s acid rock through Hawkwind's own "space rock", 70s punk, 80s electro-ecstasy, 90s techno and beyond. Born of Notting Hill's summer of love in 1969 (when their first gig was also mine), Hawkwind then detonated that of the raves two decades later – so that everyone was there for Hawkeaster this weekend: space hippies who heard them play free festivals each solstice at Stonehenge, heavy-gauge bikers who tried to defend them from the police; plus now 40-something ecstasy-heads, still determinedly tri-coloured mohican punks and a new crop of teenagers and techies. (And of course the usual, modest, quota of queue-pushing meatheads and middle-managers.)

"What is the Hawkwind family?" asked one fan at a spoof of BBC's Question Time, wherein the band took queries. "Well, it's you people," replied Hawkwind's bandleader and muse Dave Brock, now 71, referring to the gathering but also his wife Kris who manages the band, her mother Margaret who sells tickets, Melody who looks after his huge dogs and handles merchandise … and many others.

So space rock is a family business – and when a band becomes renowned for benefit gigs, the family also includes people like the Sea Shepherd environmental direct action group, whose organiser used Question Time to report on a vessel that parried a whaler in the Antarctic to such an extent its winter kill was reduced from 1,100 to 100 whales (tickets were on sale for an upcoming Sea Shepherd benefit to feature "members of Hawkwind").

Basically, we were reminded this weekend, Hawkwind is the closest Britain ever had to the tribal cult of the Grateful Dead, the enduring whole greater than the sum of its multifarious parts.

Question Time proceeded. "Will any Stonehenge gigs be released on DVD?" Brock responded by recalling "that time the police chased us up the A36, blocking the roads, nicking people, plastic cuffs and all. We drove my van across the field – helipcopters … fuckin' hell! Then we pulled over in a lay-by for a nice cup of tea – but I digress …"

It was during those Stonehenge days that Hawkwind released Warrior on the Edge of Time, one of the greatest albums of all time, never mind its edge. Issued in 1975, the record constituted a zenith of that uniquely British entwinement of driving rock with vast symphonic scale; it was wrapped in the first four-way gatefold cover; it was a definitive convergence of Brock's guitar, the ethereal synthesiser of Simon House and the impenitent bass of "Lemmy" Kilminster, for whom Warrior was a studio farewell with Hawkwind, before he formed Motörhead.

"The album was a great landmark in rock'n'roll history, and it'll be amazing to play it like this," said Hawkwind's most recent addition, Niall Hone on guitars and bass, who lives three minutes up the road in Seaton, organising vantage points in the audience for his 11-year-old daughter and nine-year-old son. This was the plan, the focus and kernel of the festival: to perform, on Saturday and Sunday nights, the album in its entirety - by way of launching a tour beginning on Tuesday, and a new commemorative edition of the record, out in May. Quite a way to mark a weekend whose theme is intended to be resurrection, or at least resurgence.

"Is it a milestone or a millstone?" wondered Brock in the aftermath on Easter Monday. "Looking back has been interesting, but our mission is to go forwards … Onward!"

Indeed, the "family" also comprises scores of musicians who have made up the greatest institution in British rock after 43 years – past and, more potently, present. Passed on, like original lead guitarist Huw Lloyd Langton who died in December last year and whose gracious widow Marion arrived to listen (and even dance onstage); and very much alive, like "Dead Fred" Phillip Reeves who returned to play synthesisers and violin. And the current line-up: Brock, Hone, long-standing drummer Richard Chadwick, Mr Dibs on bass and Tim Blake, once of Gong – Hawkwind's "cousin" band, in a way – on theremin and keyboards. During Saturday afternoon, Chadwick, Dibs and Blake had played a set with their band TOSH (Technicians of Spaceship Hawkwind) which had included Lloyd Langton's Waiting for Tomorrow, after which Dibs said: "God bless you Huw, miss you, man".

Then came Here and Now, an excellent offshoot from Gong, performing two classics: "Floating Anarchy Radio" and "Opium for the People". Yet still a few fans mooched around the pubs and chippies of Seaton; or stayed to smoke in the tipis or seaside B&B rooms that had been sold out for months. But then came the main event.

Dave Brock is nowadays a thoughtful, affable but disgruntled English country counter-gentleman living in the rural isolation of Hawkwind's intergalactic HQ and studio not far from here; though himself from Twickenham, he lived in Seaton as did his parents, and he takes time out to visit their elderly neighbours. Brock does not only nurture talent, but also the rage he must once have felt to write such classics as Motorway City and Urban Guerilla – and in Mr Dibs he has done both. Scary to behold on stage, less so in the flesh, Dibs – with his giant frame – was a roadie invited to live his dream and join the band, and a song of his called Seasons, which opens the new album Onward, blows the evening into high gear.

A diatribe against "the fevered dreams of madmen", Dibs growling on an electric 'cello, it is the political introit for a time in desperate need of such incantations, but which has all but forgotten how to write them – played against a projected backdrop of demonic scenes of warfare, strife, protest, riot police, British bobbies and a barrage of words: "oil", "dollar", "trap", "greed". A bold statement by the band: we still do this - and thence to Warrior on the Edge of Time.

The album was inspired by science fiction writer Michael Moorcock, his theory of the "multiverse" and eternal battle between order and chaos (much of it grounded in Greek myth and, since, respectable astronomy). The balance must be struck by a "champion", who blends, well … Ulysses with Dr Who, kind of. Hawkwind's hallmark dancers – enlacing glamour, Marvel Comics and space panto – act out the battle with axes and the champion's sword, as either bikini-clad versions of Wagner's Friea and Dido of Carthage, or hogs with ram's horns or sun-goddesses on stilts.

The overture, "Assault and Battery", establishes a theme: Chadwick's drumfire, a cannonade that propels and impels the music throughout. It is amazing that such an apparently slight and elven man, with waist-length hair and an aura straight from Lord of the Rings, can strike at such an unrelenting gallop – driving the beat with what felt like one long drum-burst – a metronome unleashed.

The track progresses into the album's commanding height, the epic "Golden Void Part II" - an edifice of vast but lyrical proportions, which enabled Blake, looking professorially feral, to soar the heights on his range of devices of which he is these days the unrivalled magician – above all the theramin: bewitching, sometimes sepulchral. A saxophone player was introduced to improve by far on the original studio part: Sosna from the Warsaw-based band HipiersoniK.

"Magnu" – which many of us present think of as Side B, Track 1 – is Brock's adaptation of, and homage to, Shelley's "Song to Apollo", which he played with cogency and especial ardour. Although Dibs is in a way the current band's incarnation of Lemmy, the original bassist's lines were shared between – and intensified by – himself and Hone for much of the album's resurgence, and the tracks that followed. Both played at gale force; so that the doubling-up on bass guitar gave the whole enterprise more muscle, drive, depth and propulsion than the Hawkwind of 1975.

Hone said, when both sets were done on Sunday night: "I hope we kept some of the album's charm" – and it was an apposite, if surprising, choice of word: yes, there is exactly that, a decorum born of balancing severity of purpose, musicianship for the sheer joy of it – and pastiche. For Hawkwind may sound apocalyptic, but they are also funny, and humour is a rare commodity in rock'n'roll.

Hawkwind playing at Hawkeaster, 2013. Photograph: Captain Smurf

There is of course a driving force behind all this, a pillar down the decades and over this weekend: Captain Brock wore a hat that made him look like a scarecrow, and wields a beautifully-painted – and beautifully-played – guitar. The sway of Hawkwind's hurdy-gurdy man established itself at the start, commanding the rhythm and taking a crisp but spectral lead break on "You'd Better Believe It". Brock gave the album an eye of the storm with his acoustic delivery of "The Demented Man", and urged the night to a vehement close with "Spirit of the Age" on Saturday, then the perennial "Silver Machine" on Sunday.

Over two nights, perhaps even more could have been made of Warrior live, had not an estimable decision been made to stick to, and re-invent, the original. "Golden Void" has a grandeur that could have sustained a 15-minute live edition, even further deepened by Dibs's electric cello. The drum roll on Side B could have been extended by Chadwick into a full-blown, Grateful Dead-style solo. Brock could have allowed himself forays on guitar even beyond the flourishes he did.

But this was not the plan, and as things were, faithful in shape to the album's structure, these performances not only revived "Warrior on the Edge of Time", they wrestled with and augmented it. Truth is, it never sounded better – and why should not these things be played even better now than they were in 1975?

But "what will music sound like in 2030?" the band was asked during Question Time. "Will there be electricity in 2030?" replied Blake. "The way the politicians are going, will be there be a 2030?" added Mr Dibs. "What is the meaning of life?" asked a fan. "Pass", replied Brock in his scarecrow hat, "next question".